analysis of variance noteshells

# analysis of variance noteshells - Two-Way Analysis of...

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1 Two-Way ANOVA 1 Two-Way Analysis of Variance Section 11.2 Two-Way ANOVA 2 Two-Way ANOVA h Earlier we classified the data one way (by dimple design or by hospital). h In some problems, there may be several experimental factors and the data can be classified several ways. h The ANOVA procedure can be extended to this.

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2 Two-Way ANOVA 3 The parachute factory h Four suppliers manufacture the synthetic thread we use to weave parachutes in our factory. h We use two types of looms, the Jetta and the Turk. h We want to know if the fabric strength depends on supplier, on loom, or if it is combinations of supplier and loom. Two-Way ANOVA 4 Brake job promotion h A chain of auto stores puts their standard brake job on sale. h In some places, they promote a lower labor price. In some, a lower parts price. Some others just promote the lower total price. h Which works best? Is it the same across the country, or does it depend on region ?
3 Two-Way ANOVA 5 The Two-Way Design h We allow for potential differences due to different levels of factor A. h We also allow for potential differences due to different levels of factor B. h We also recognize that these differences may not be consistent so combinations of factor A and B may be what matters. Two-Way ANOVA 6 Notation h Let’s say there are r levels of factor A and c levels of factor B. h We thus have a total of rc combinations of the two factors. h We will only look at problems where there are more than one observation for each combination, call it n’ replicates per cell.

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4 Two-Way ANOVA 7 Data organization Data are organized in a rectangle. 1. There will be c columns, one for each level of factor B. 2. Each of the r levels of factor A will have a “sample” of n’ rows. 3. There are thus r n’ total rows of data. Two-Way ANOVA 8 Parachute2.xls Loom Type Supplier 1 Supplier 2 Supplier 3 Supplier 4 Jetta 20.6 22.6 27.7 21.5 Jetta 18.0 24.6 18.6 20.0 Jetta 19.0 19.6 20.8 21.1 Jetta 21.3 23.8 25.1 23.9 Jetta 13.2 27.1 17.7 16.0 Turk 18.5 26.3 20.6 25.4 Turk 24.0 25.3 25.2 19.9 Turk 17.2 24.0 20.8 22.6 Turk 19.9 21.2 24.7 17.5 Turk 18.0 24.5 22.9 20.4 c = 4, r = 2 and n’ = 5
5 Two-Way ANOVA 9 Means plot h A good exploratory tool is to plot the average value of x that occurs at each combination of factors. h

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analysis of variance noteshells - Two-Way Analysis of...

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